This work presents a new device concept, the Multi-Channel Monolithic-Cascode high-electron-mobility transistor (MC2-HEMT), which monolithically integrates a low-voltage, enhancement-mode (E-mode) HEMT based on single 2DEG channel and a high-voltage, depletion-mode (D-mode) HEMT based on stacked 2DEG multi-channel. This device can exploit the low sheet resistance of the multi-channel, realize an E-mode gate control, and completely shield the gate region from high electric field. It also obviates the need for nanometer-sized fin-shaped gates used in prior multi-channel HEMTs, thus relaxing the lithography requirement. We experimentally demonstrated the multi-kilovolt AlGaN/GaN MC2-HEMTs on a 5-channel wafer with breakdown voltage from 3.45 kV up to over 10 kV. The 10-kV MC2-HEMTs show a 1.5-V threshold voltage and a $40\text{-m}\Omega\cdot \text{cm}^{2}$ specific on-resistance, which is $\sim 2.5$-fold smaller than that of 10-kV SiC MOSFETs and well below the SiC 1-D unipolar limit. To date, this is the first report of $3\text{-kV}+$ E-mode GaN devices, and our MC2-HEMTs show the highest Baliga's figure-of-merits in all $6.5\text{-kV}+$ transistors. The MC2-HEMT is also applicable to other materials, e.g., (Al)GaO and Al(Ga)N, as a platform design for multi-channel power transistors.